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The Art of Problem Posing [Paperback]

Stephen I. Brown (Author), Marion I. Walter (Author)
5.0 out of 5 stars  See all reviews (2 customer reviews)

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Book Description

December 9, 2004 0805849777 978-0805849776 3
The new edition of this classic book describes and provides a myriad of examples of the relationships between problem posing and problem solving, and explores the educational potential of integrating these two activities in classrooms at all levels. The Art of Problem Posing, Third Edition encourages readers to shift their thinking about problem posing (such as where problems come from, what to do with them, and the like) from the "other" to themselves and offers a broader conception of what can be done with problems. Special features include: an exploration of the logical relationship between problem posing and problem solving; sketches, drawings, and diagrams that illustrate the schemes proposed; and a special section on writing in mathematics.

In the updated third edition, the authors specifically:
*address the role of problem posing in the NCTM Standards;
*elaborate on the concept of student as author and critic;
*include discussion of computer applications to illustrate the potential of  technology to enhance problem posing in the classroom;
*expand the section on diversity/multiculturalism; and
*broaden discussion of writing as a classroom enterprise.

This book offers present and future teachers at the middle school, secondary school, and higher education levels ideas to enrich their teaching and suggestions for how to incorporate problem posing into a standard mathematics curriculum.

Frequently Bought Together

Customers buy this book with How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) $11.79

The Art of Problem Posing + How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)


Editorial Reviews

Review

When first published in 1983,...provided an innovative approach to mathematics education and problem solving. The third edition features several new highlights, including computer examples that show how technology affects problem posing, discussion of the concept of student as author and critic, and analysis of how the 'standards' in math education incorporate problem-posing techniques.
ED - Harvard Graduate School of Education

The text is easy to read and actively involves the reader. The Art of Problem Solving has the potential to influence significantly the way teachers think about the nature of mathematics and what it means to 'do' mathematics. The authors invision that this will, in turn, influence mathematics students of all ages as they engage in solving problems they themselves have posed.

Mathematics Teacher

The audience for this book is any college mathematics students, present and future teachers of mathematics, as well as any person interested in problem posing.
School Science and Mathematics Journal


Product Details

  • Paperback: 192 pages
  • Publisher: Routledge; 3 edition (December 9, 2004)
  • Language: English
  • ISBN-10: 0805849777
  • ISBN-13: 978-0805849776
  • Product Dimensions: 9.1 x 6.1 x 0.4 inches
  • Shipping Weight: 10.6 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #1,074,065 in Books (See Top 100 in Books)

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Customer Reviews

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9 of 9 people found the following review helpful:
5.0 out of 5 stars provides a method for exploring mathematical problems as well as posing them, January 16, 2007
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This review is from: The Art of Problem Posing (Paperback)
The Art of Problem Posing is a great book. The authors provide a step by step method for learning about, and solving problems in, mathematics. The method is as follows:

Level O:

Choose a starting point ie a problem or a concept in math

Level 1:

Define the attributes of a problem or concept

Level 2:

Ask what if not for each concept.

Level 3:

Ask Questions about the results of 0 - 2.

Level 4:

Analyze (solve) the problem

The authors use fairly accessible math in the process of explaining their techniques, including the Pythagorean Theorem and a few other concepts that most people will know.

I want to emphasize that this book is not just about problem posing; it also offers a technique for problem solving. The authors note that the two cannot really be completely separated.
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2 of 2 people found the following review helpful:
5.0 out of 5 stars Shelve with Polya, August 2, 2010
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This review is from: The Art of Problem Posing (Paperback)
Written at an elementary level, but the insights are fantastic. I don't know if the mathematically astute think analogously to the manner taught in this book, but it seems there would be something here for everyone -- excluding maybe professionals. Also, the book is so short that it can be read (and re-read if need be) speedily until the strategies are second nature. I was as excited reading this as I was Polya's series -- but the two cover different aspects of mathematical investigation. I'm glad this book was written and that I found it!
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Inside This Book (learn more)
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Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
mathematics teaching, art ofproblem posing, dynamic geometry program, different rectangles, distributive property, two given numbers, starting lengths, adjacent terms
Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Geometer's Sketchpad, National Council of Teachers of Mathematics, Reconstructing School Mathematics, American Mathematical Monthly, Mathematics Teacher, Marion Walter, Fostering Mathematical Curiosity, Supreme Court, George Polya, Princeton University Press, Deborah Moore-Russo, Pythagorean Numbers, Scientific American, San Francisco, Peter Lang
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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